Uncertainty Relation in Quantum Mechanics with Quantum Group(3)

We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the underlying noncom

Onethenobtainsforthescalarproduct:

0|(an)

with

[r]q!:=[1]q·[2]q·[3]q·...·[r]qand[p]q:=rn·...·(a1)r1r1(a 1)·...·rn(a n)|0 =i=1n [ri]q!q2p 1(5)

unlikeusingasusualordinarycomplexintegrationforthebosoniccaseandBerezinintegrationforthefermioniccase2weakeningthisrestriction,onemaygeneralisabletheansatz

Eqs.71

3